Ukraine has accused Russia of carrying out an armed invasion by sending naval forces to occupy Sevastopol airport in the Crimea region.
Russia's Black Sea Fleet denies its servicemen are blocking the airport.
Another Crimean airport, Simferopol, has also been occupied by armed men, thought to be pro-Russia militia.
Relations between the two countries have been strained since Viktor Yanukovych was ousted as Ukrainian president last week.
Mr Yanukovych is now in Russia and expected to hold a news conference later in the city of Rostov-on-Don, near the Ukrainian border.
He disappeared after leaving office but resurfaced in Russia on Thursday, asserting that he is still Ukraine's lawful president.
Ukraine's general prosecutor has said he will ask Russia to extradite Mr Yanukovych, if it is confirmed that he is still there.
In other developments:
- The BBC has seen eight trucks with the black plates of the Russian army moving towards Simferopol
- Unconfirmed reports say eight Russian military helicopters have arrived in Sevastopol
- Ukraine's central bank has put a 15,000 hryvnia (1,000 euro; £820) limit on daily cash withdrawals
- Armed Forces chief Yuriy Ilyin, appointed earlier this month by Mr Yanukovych, is sacked
- Ukraine's parliament calls on the UN Security Council to discuss the unfolding crisis in Crimea
Lynchpin of struggle
These tensions between Russia and Ukraine in the wake of Mr Yanukovych's departure have been particularly evident in Crimea, Ukraine's only Russian-majority region.
The BBC's Bridget Kendall, in Moscow, says the Crimea is becoming the lynchpin of a struggle between Ukraine's new leaders and those loyal to Russia.
Ukrainian Interior Minister Arsen Avakov said Russian soldiers had arrived in Sevastopol military airport near Russia's Black Sea Fleet Base on Friday morning.
The men were patrolling outside, backed up by armoured vehicles, but Ukrainian military and border guards remained inside, Mr Avakov said.
"I consider what has happened to be an armed invasion and occupation in violation of all international agreements and norms," Mr Avakov said on his Facebook page.
Armed men also arrived at Simferopol airport overnight, some carrying Russian flags.
A man called Vladimir told Reuters news agency he was a volunteer helping the group there, though he said he did not know where they came from.
"I'm with the People's Militia of Crimea. We're simple people, volunteers," he said.
Andriy Parubiy, acting chairman of Ukraine's National Security Council, has claimed that both airports are now back under the control of Ukrainian authorities.
The airport occupation is latest in a series of moves to raise fears of unrest in Crimea, which traditionally leans towards Russia.
On Thursday, a group of unidentified armed men entered Crimea's parliament building by force, and hoisted a Russian flag on the roof.
The Crimean parliament later announced it would hold a referendum on expanding the region's autonomy from Ukraine on 25 May.
Russian President Vladimir Putin has urged his government to maintain relations with Kiev, but he is also giving the Crimean government humanitarian aid.
US Secretary of State John Kerry has called on all sides to "step back and avoid any kind of provocations".
On top of its political problems, Ukraine also faces huge financial hurdles.
It says it needs $35 billion over the next two years to avoid default on its loans.
Russia has suspended the next instalment of a $15bn loan because of the political uncertainty.
Switzerland and Austria announced on Friday that it had launched an investigation against Mr Yanukovych and his son Aleksander for "aggravated money laundering".
Austria also said it had frozen the assets of 18 Ukrainians suspected of violating human rights and involvement in corruption. It did not give any names.
Crimea - where ethnic Russians are in a majority - was transferred from Russia to Ukraine in 1954.
Ethnic Ukrainians loyal to Kiev and Muslim Tatars - whose animosity towards Russia stretches back to Stalin's deportations during World War Two - have formed an alliance to oppose any move back towards Moscow.
Russia, along with the US, UK and France, pledged to uphold the territorial integrity of Ukraine in a memorandum signed in 1994.